Let $M$ be a real analytic variety (if someone is concerned about distinction between "real analytic spaces" and "real analytic varieties" in real analytic geometry, let's assume that $M$ is both "variety" and "space"). I was sure it is well-known that higher cohomology of any real analytic coherent sheaf over $M$ vanish.

The argument is standard: by Grauert, a real analytic variety is the set of real points in a Stein variety $M_{C}$ with an anticomplex involution $v$. A coherent sheaf over $M$ is the set of $v$-invariant sections of a $v$-equivariant coherent sheaf $F_{C}$ on $M_{C}$, and $F_C$ has vanishing cohomology because $M_C$ is Stein.

Recently I needed a reference to this fact, and I could not find it. I would be extremely grateful for a reference!

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